Don’t worry if it is not filtered. If you store it in the fridge, it lasts months without issues. When you get to the bottom of the jar, be mindful of any exposed “bits” or “moisture”. This will start to rot if in contact with air. You can either pour a bit of olive oil or more tallow to cover exposed bits, or see if you can move things around in the jar, so that everything is coated/submerged in fat.

I’m sure it won’t hurt to have some nice bits in there but If you use it for baking it might add some stank to something that you want sweet.

What I do is pour the extra fat while liquid into a tall, narrow bottom container (plastic or metal pint glass) and put it in the freezer. Once it’s all hard i’ll run some water over the container to get it out. Once out, I cut off the extra bits that fell to the bottom. I then treat them the same as broth; freeze in ice cube tray, then transfer to freezer bag and freeze.